多个组的密度图之间的交集

Question

我正在使用 ggplot / easyGgplot2 创建两组的密度图。我想知道两条曲线之间有多少交点的度量或指示。我什至可以使用没有曲线的任何其他解决方案，只要它允许我衡量哪些组更不同（几个不同的数据组）。

在 R 中有什么简单的方法可以做到这一点吗？

例如使用生成此图的示例

如何估算两者共有的面积百分比？

ggplot2.density(data=weight, xName='weight', groupName='sex',
    legendPosition="top",
    alpha=0.5, fillGroupDensity=TRUE )

Answer 1

首先，制作一些数据以供使用。在这里，我们将从内置 iris 数据集中查看两种植物的花瓣宽度。

## Some sample data from iris
dat <- droplevels(with(iris, iris[Species %in% c("versicolor", "virginica"), ]))

## make a similar graph
library(ggplot2)
ggplot(dat, aes(Petal.Width, fill=Species)) +
  geom_density(alpha=0.5)

求交集的面积，可以用approxfun近似描述交集的函数。然后，将其集成到获取区域中。由于这些是密度曲线，它们的面积为 1（ish），因此积分将是重叠百分比。

## Get density curves for each species
ps <- lapply(split(dat, dat$Species), function(x) {
    dens <- density(x$Petal.Width)
    data.frame(x=dens$x, y=dens$y)
})

## Approximate the functions and find intersection
fs <- sapply(ps, function(x) approxfun(x$x, x$y, yleft=0, yright=0))
f <- function(x) fs[[1]](x) - fs[[2]](x)   # function to minimize (difference b/w curves)
meet <- uniroot(f, interval=c(1, 2))$root  # intersection of the two curves

## Find overlapping x, y values
ps1 <- is.na(cut(ps[[1]]$x, c(-Inf, meet)))
ps2 <- is.na(cut(ps[[2]]$x, c(Inf, meet)))
shared <- rbind(ps[[1]][ps1,], ps[[2]][ps2,])

## Approximate function of intersection
f <- with(shared, approxfun(x, y, yleft=0, yright=0))

## have a look
xs <- seq(0, 3, len=1000)
plot(xs, f(xs), type="l", col="blue", ylim=c(0, 2))

points(ps[[1]], col="red", type="l", lty=2, lwd=2)
points(ps[[2]], col="blue", type="l", lty=2, lwd=2)

polygon(c(xs, rev(xs)), y=c(f(xs), rep(0, length(xs))), col="orange", density=40)

## Integrate it to get the value
integrate(f, lower=0, upper=3)$value
# [1] 0.1548127

Answer 2

我喜欢前面的答案，但这可能更直观一点，而且我确保使用了公共带宽：

library ( "caTools" )

# Extract common bandwidth
Bw <- ( density ( iris$Petal.Width ))$bw

# Get iris data
Sample <- with ( iris, split ( Petal.Width, Species ))[ 2:3 ]

# Estimate kernel densities using common bandwidth
Densities <- lapply ( Sample, density,
                      bw = bw,
                      n = 512,
                      from = -1,
                      to = 3 )

# Plot
plot( Densities [[ 1 ]], xlim = c ( -1, 3 ),
      col = "steelblue",
      main = "" )
lines ( Densities [[ 2 ]], col = "orange" )

# Overlap
X <- Densities [[ 1 ]]$x
Y1 <- Densities [[ 1 ]]$y
Y2 <- Densities [[ 2 ]]$y

Overlap <- pmin ( Y1, Y2 )
polygon ( c ( X, X [ 1 ]), c ( Overlap, Overlap [ 1 ]),
    lwd = 2, col = "hotpink", border = "n", density = 20) 

# Integrate
Total <- trapz ( X, Y1 ) + trapz ( X, Y2 )
(Surface <- trapz ( X, Overlap ) / Total)
SText <- paste ( sprintf ( "%.3f", 100*Surface ), "%" )
text ( X [ which.max ( Overlap )], 1.2 * max ( Overlap ), SText )

多个组的密度图之间的交集

Intersection between density plots of multiple groups

r

plot

ggplot2

density-plot